The Sobolev embedding constant on Lie groups. (March 2022)

• Record Type: Journal Article
• Authors: Bruno, Tommaso; Peloso, Marco M.; Vallarino, Maria
• Is Part Of: Nonlinear analysis. Volume 216(2022)
• Publication Date: 2022-03
• Subjects: 26D10 -- 43A80 -- 46E35; Lie groups -- Sobolev embeddings -- Best constant -- Moser–Trudinger inequality; Mathematical analysis -- Periodicals; Functional analysis -- Periodicals; Nonlinear theories -- Periodicals; Analyse mathématique -- Périodiques; Analyse fonctionnelle -- Périodiques; Théories non linéaires -- Périodiques; Functional analysis; Mathematical analysis; Nonlinear theories; Periodicals; Electronic journals; 515.7248
• DOI: 10.1016/j.na.2021.112707
• Languages: English
• ISSNs: 0362-546X

Abstract

Abstract: In this paper we estimate the Sobolev embedding constant on general noncompact Lie groups, for sub-Riemannian inhomogeneous Sobolev spaces endowed with a left invariant measure. The bound that we obtain, up to a constant depending only on the group and its sub-Riemannian structure, reduces to the best known bound for the classical inhomogeneous Sobolev embedding constant on R d . As an application, we prove local and global Moser–Trudinger inequalities.